As a number of detector rows increases, the increasing cone angle has become an important factor in a practical reconstruction algorithm. In this regard, prior art technologies have embraced an exact helical cone beam algorithm of the shift invariant FBP type (Katsevich algorithm), which use only data within the helical PI-intervals. In other words, data are used only within the N-PI window, where N=1, 3, . . . , is the number of helical half-turns.
The N-PI window weighting has the following disadvantages. Since some measured data located outside the N-PI window is not used, extra X-ray dose is unnecessarily imposed on the patient. In addition, because all data within the N-PI window is used with the same weight, an algorithm generally becomes more sensitive to patient motion and imperfections of real data despite the noise reduction. Lastly, the N-PI reconstruction limits the helical pitch. For example, pitches in the range of 0.75-0.85 are too fast to be used with the 3-PI window and are suboptimal to use with the 1-PI window since only a small fraction of data is utilized.
Meanwhile, 2D fan beam redundancy weighting has advantages such as easy adjustment to the helical pitch and smooth transition from 0 to 1. That is, an algorithm is more stable to patient motion and imperfections of real data. On the other hand, when motion is present, exactness needs to be balanced with stability to motion. Prior art approaches generally disregard increasing cone angle and are not suitable for fully 3D reconstruction.